{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Dissipation in Runge-Kutta Methods"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as pt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "def rk4_step(y, t, h, f):\n",
        "    k1 = f(t, y)\n",
        "    k2 = f(t+h/2, y + h/2*k1)\n",
        "    k3 = f(t+h/2, y + h/2*k2)\n",
        "    k4 = f(t+h, y + h*k3)\n",
        "    return y + h/6*(k1 + 2*k2 + 2*k3 + k4)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Consider the second-order harmonic oscillator\n",
        "\n",
        "$$u''=-u$$\n",
        "\n",
        "with initial conditions $u(0) = 1$ and $u'(0)=0$.\n",
        "\n",
        "$\\cos(x)$ is a solution to this problem.\n",
        "\n",
        "`f` below gives the right-hand side for this ODE converted to first-order form:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "def f(t, y):\n",
        "    u, up = y\n",
        "    return np.array([up, -u])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Now, we use 4th-order Runge Kutta to integrate this system over \"many\" time steps:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "times = [0]\n",
        "y_values = [np.array([1,0])]\n",
        "\n",
        "h = 0.5\n",
        "t_end = 800\n",
        "\n",
        "while times[-1] < t_end:\n",
        "    y_values.append(rk4_step(y_values[-1], times[-1], h, f))\n",
        "    times.append(times[-1]+h)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Lastly, plot the computed solution:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f18e0f80470>]"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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H9lim4jv+9ubNy8c++IPz6q03Z3/+582+7dtiP/Hsnb0FOfvdzBenf+yPmf2hPxT36Ran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\nQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f18e3012cc0>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "y_values = np.array(y_values)\n",
        "\n",
        "pt.figure(figsize=(15,5))\n",
        "pt.plot(times, y_values[:, 0])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": false
      },
      "source": [
        "What do you observe?"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.5.1+"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}